10.5.4.5 Probabilistic Projections - Global Mean

A number of methods for providing probabilistic climate change projections, both for global means (discussed in this section) and geographical depictions (discussed in the following section) have emerged since the TAR.

Methods of constraining climate sensitivity using observations of present-day climate are discussed in Section 10.5.4.2. Results from both the AR4 multi-model ensemble and from perturbed physics ensembles suggest a very low probability for a climate sensitivity below 2°C, despite exploring the effects of a wide range of alternative modelling assumptions on the global radiative feedbacks arising from lapse rate, water vapour, surface albedo and cloud (Bony et al., 2006; Soden and Held, 2006; Webb et al., 2006; Box 10.2). However, exclusive reliance on AOGCM ensembles can be questioned on the basis that models share components, and therefore errors, and may not sample the full range of possible outcomes (e.g., Allen and Ingram, 2002).

Observationally constrained probability distributions for climate sensitivity have also been derived from physical relationships based on energy balance considerations, and from instrumental observations of historical changes during the past 50 to 150 years or proxy reconstructions of surface temperature during the past millennium (Section 9.6). The results vary according to the choice of verifying observations, the forcings considered and their specified uncertainties, however, all these studies report a high upper limit for climate sensitivity, with the 95th percentile of the distributions invariably exceeding 6°C (Box 10.2). Frame et al. (2005) demonstrate that uncertainty ranges for sensitivity are dependent on the choices made about prior distributions of uncertain quantities before the observations are applied. Frame et al. (2005) and Piani et al. (2005) show that many observable variables are likely to scale inversely with climate sensitivity, implying that projections of quantities that are inversely related to sensitivity will be more strongly constrained by observations than climate sensitivity itself, particularly with respect to the estimated upper limit (Allen et al., 2006b).

In the case of transient climate change, optimal detection techniques have been used to determine factors by which hindcasts of global surface temperature from AOGCMs can be scaled up or down while remaining consistent with past changes, accounting for uncertainty due to internal variability (Section 9.4.1.6). Uncertainty is propagated forward in time by assuming that the fractional error found in model hindcasts of global mean temperature change will remain constant in projections of future changes. Using this approach, Stott and Kettleborough (2002) find that probabilistic projections of global mean temperature derived from UKMO-HadCM3 simulations were insensitive to differences between four representative SRES emissions scenarios over the first few decades of the 21st century, but that much larger differences emerged between the response to different SRES scenarios by the end of the 21st century (see also Section 10.5.3 and Figure 10.28). Stott et al. (2006b) show that scaling the responses of three models with different sensitivities brings their projections into better agreement. Stott et al. (2006a) extend their approach to obtain probabilistic projections of future warming averaged over continental-scale regions under the SRES A2 scenario. Fractional errors in the past continental warming simulated by UKMO-HadCM3 are used to scale future changes, yielding wide uncertainty ranges, notably for North America and Europe where the 5 to 95% ranges for warming during the 21st century are 2°C to 12°C and 2°C to 11°C respectively. These estimates do not account for potential constraints arising from regionally differentiated warming rates. Tighter ranges of 4°C to 8°C for North America and 4°C to 7°C for Europe are obtained if fractional errors in past global mean temperature are used to scale the future continental changes, although this neglects uncertainty in the relationship between global and regional temperature changes.

Allen and Ingram (2002) suggest that probabilistic projections for some variables may be made by searching for ‘emergent constraints’. These are relationships between variables that can be directly constrained by observations, such as global surface temperature, and variables that may be indirectly constrained by establishing a consistent, physically based relationship which holds across a wide range of models. They present an example in which future changes in global mean precipitation are constrained using a probability distribution for global temperature obtained from a large EMIC ensemble (Forest et al., 2002) and a relationship between precipitation and temperature obtained from multi-model ensembles of the response to doubled atmospheric CO2. These methods are designed to produce distributions constrained by observations, and are relatively model independent (Allen and Stainforth, 2002; Allen et al., 2006a). This can be achieved provided the inter-variable relationships are robust to alternative modelling assumptions Piani et al. (2005) and Knutti et al. (2006) (described in Section 10.5.4.2) follow this approach, noting that in these cases the inter-variable relationships are derived from perturbed versions of a single model, and need to be confirmed using other models.

A synthesis of published probabilistic global mean projections for the SRES scenarios B1, A1B and A2 is given in Figure 10.28. Probability density functions are given for short-term projections (2020–2030) and the end of the century (2090–2100). For comparison, normal distributions fitted to results from AOGCMs in the multi-model archive (see Section 10.3.1) are also given, although these curve fits should not be regarded as PDFs. The five methods of producing PDFs are all based on different models and/or techniques, described in Section 10.5. In short, Wigley and Raper (2001) use a large ensemble of a simple model with expert prior distributions for climate sensitivity, ocean heat uptake, sulphate forcing and the carbon cycle, without applying constraints. Knutti et al. (2002, 2003) use a large ensemble of EMIC simulations with non-informative prior distributions, consider uncertainties in climate sensitivity, ocean heat uptake, radiative forcing and the carbon cycle, and apply observational constraints. Neither method considers natural variability explicitly. Stott et al. (2006b) apply the fingerprint scaling method to AOGCM simulations to obtain PDFs which implicitly account for uncertainties in forcing, climate sensitivity and internal unforced as well as forced natural variability. For the A2 scenario, results obtained from three different AOGCMs are shown, illustrating the extent to which the Stott et al. PDFs depend on the model used. Harris et al. (2006) obtain PDFs by boosting a 17-member perturbed physics ensemble of the UKMO-HadCM3 model using scaled equilibrium responses from a larger ensemble of simulations. Furrer et al. (2007) use a Bayesian method described in Section 10.5.4.7 to calculate PDFs from the AR4 multi-model ensemble. The Stott et al. (2006b), Harris et al. (2006) and Furrer et al. (2007) methods neglect carbon cycle uncertainties.

Figure 10.28. Probability density functions from different studies for global mean temperature change for the SRES scenarios B1, A1B and A2 and for the decades 2020 to 2029 and 2090 to 2099 relative to the 1980 to 1999 average (Wigley and Raper, 2001; Knutti et al., 2002; Furrer et al., 2007; Harris et al., 2006; Stott et al., 2006b). A normal distribution fitted to the multi-model ensemble is shown for comparison.

Two key points emerge from Figure 10.28. For the projected short-term warming (i) there is more agreement among models and methods (narrow width of the PDFs) compared to later in the century (wider PDFs), and (ii) the warming is similar across different scenarios, compared to later in the century where the choice of scenario significantly affects the projections. These conclusions are consistent with the results obtained with SCMs (Section 10.5.3).

Additionally, projection uncertainties increase close to linearly with temperature in most studies. The different methods show relatively good agreement in the shape and width of the PDFs, but with some offsets due to different methodological choices. Only Stott et al. (2006b) account for variations in future natural forcing, and hence project a small probability of cooling over the next few decades not seen in the other PDFs. The results of Knutti et al. (2003) show wider PDFs for the end of the century because they sample uniformly in climate sensitivity (see Section 9.6.2 and Box 10.2). Resampling uniformly in observables (Frame et al., 2005) would bring their PDFs closer to the others. In sum, probabilistic estimates of uncertainties for the next few decades seem robust across a variety of models and methods, while results for the end of the century depend on the assumptions made.